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Coordinate transformation between
Everest and WGS – 84 datums – A parametric approach
Datum transformation parameters
The difference between positions in terms of an individual local datum and positions in terms of a global datum may be of the order of several hundred meters, and may vary considerably even for a single local datum. If the local survey network has variable quality or does not have a continuous landmass, a country may effectively have a number of local datums, requiring a number of different transformations to the global datum.
With the increasing exchange of geographic information local and globally, positions need to be available in terns of both a local and global datums. The process of mathematically converting positions from one datum to the other is known as datum transformation.
Datum transformation parameters define functional relationship between two reference frames. The GPS derived coordinates and local terrestrial coordinates of collocated points may be processed together using an appropriate transformation model. The outcome of the processing would be a set of quantities termed as transformations parameters which could be used for converting coordinates from one datum to the other and vice-versa. The combination of data sets from two or more different sources is strictly an adjustment problem and must be solved by applying appropriate technique.
Transformation procedure
There are a number of ways to mathematically transform positions from one datum to another, but they all require “common points”. Common points are surveyed points that have known positions in terms of both the local and the global datum. The achievable accuracy of the datum transformation will be determined by the number, distribution and accuracy of these common points and the transformation technique adopted. Generally speaking, the greater the accuracy required, the more common points are needed.
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Selection of common points
The present study was focused on estimation of transformation parameters between Everest & WGS-84 datum in order to convert the existing topo sheets to WGS-84 series maps without loss of generality. To accomplish the job 300 existing Great Trigonometrical Series ( GT ) stations, evenly distributed throughout the country were selected for GPS observations. The points were chosen in such a manner that it represent a good sample of the true relationship between the local and global datums. Since Indian triangulation network comprised of independently adjusted series with different level of accuracy i.e. primary and secondary it was highly unlikely to get a single set of transformation parameter with desirable accuracy for the entire country.
- GPS observations and data processing
A comprehensive observation plan was chalked out to ensure the smooth running of field programme. All the survey personnel involved had a tough time during the entire field duration which lasted for nearly 16 months with a short-break. Continuous GPS observations for 12-24 hrs at each station were carried out with a sampling rate of 30 seconds. Since the distance between two consecutive stations was more than 100 km nearly10,000 sq. km area was covered in one exercise involving 4 GPS receivers. The entire field observation work was evenly distributed between two independent teams, each comprised of seven personnel including reccee officers and the coordinator.
After completion of field work the observed data was processed with precise ephemerides using Bernese Version 4.2 software. WGS-84 coordinates of each observed station were determined by processing the observed GPS data in combination with two to three IGS ( International GPS Service for Geodynamics ) sites located around the country viz. Kitab, Lhasa etc. which were taken as reference stations during the processing operation. The computed coordinates along with known Everest coordinates of each observed point formed the data set for estimation of transformation parameters.
- Tranformation models
Several mathematical models have been developed which describe the functional relationship between pairs of three dimensional coordinates. Three mathematical models, namely Bursa-Wolf ( Bursa, 1962, Wolf, 1963 ), Molodensky ( Molodensky et.al., 1962 ) and Veis ( Veis, 1960 ) are noted as standard models due to their extensive use around the world over a number of years. The models differ from each other in several ways including a priori conditions, the type of coordinate used and the interpretation of results.
The GPS provides new and independent source of data. Whether or not this data will yield a satisfactory solution of terrestrial network transformation problems is dependent on the accuracy and homogeneity of local geodetic coordinates and the mathematical model employed in the estimation procedure ( Singh, S.K. 1994 ). In our case the accuracy of GPS derived coordinates of each stations have been assured by processing data with Bernese scientific software making use of precise ephemerides and keeping IGS stations as fixed sites. The Bursa-Wolf transformation model is the most popular and effective one and it has been used by several countries around the World. A typical example is South Africa where this transformation model was used to determine the relationships between various local datums and Conventional Terrestrial System ( CTS ) ( Rens, J., Merry, C.L. 1990 ). The simplicity of the Bursa-Wolf Transformation Model is another reason of applying it for our transformation problem.
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